# An Analysis Of Capital Asset Pricing Model Finance Essay

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The CAPM model plays a very vital role in the equity market these days. Since Investors are to invest in such a way which maximizes there revenues and profits and so similarly CAPM helped them a lot by calculating cost of capital and measure portfolio performance. Similarly with time by 1990 Fama and French then proposed a three factor model in which they criticized CAPM. Therefore in order to find out which methods are still widely used by many investors "Graham and Harvey (2001) "conducted a survey and according to the research 73.5 % of 392 U.S firms relies on CAPM while estimating the cost of equity. Another survey was therefore conducted by "Jong and Koedijk (2004) "and this time it was European firms. 313 firms were surveyed and 45% of them relied on CAPM. Strange to find out that still CAPM is widely used inspite of all the criticize held against it so it might be that CAPM is better then Fama and French. Now let us see what CAPM model really is and what are its main properties, its relative merits and demerits and its practical implication with respect to another famous model the Fama and French Model.

The CAPM, developed by William Sharpe (1964), Linter (1965), and Mossin (1966), CAPM has been widely used in many applications, such as evaluating the performance of many portfolios and estimating the capital cost of companies (Fama, and French, 2004, p.24). CAPM discusses on two very important factors or relationships on which it is built the SML and CML. The SML tells about the risk free rate and it suggests that higher the beta higher the return will be. Regarding securities SML determines whether they are priced or not (Review of CAPM 2007, p.4)

CML on the other hand describes about the efficient portfolio and shows investors return on an efficient portfolio.

CAPM is based on numerous assumption and these assumptions become to some sort of basis for criticism by many people as they claim them to unrealistic. The assumptions are as follows and must be kept in mind.

Investors choose their investment portfolios on the basis of expected return and variance of return over single period;

It is assumed that the diversified portfolio is held by Investors

Investors have the same estimates of mean, variance and covariance of all assets;

The capitals markets have no transaction costs;

Perfect capital market.

All assets are perfectly divisible;

Single-period transaction horizon.

No restriction on short sales;

It is also assumed as Investors can borrow and lend at the risk-free rate of return . ( means that a holding period of almost one year is required)

No Taxes

No commission

Basically the assumptions made by the CAPM focuses on the relationship between the risk (systematic Risk) and return is not as what happens in the real world in which all these decisions are made by companies and individuals

Well if we have a look at capital markets In developed countries they are efficient enough,

still chances of stock market to be priced incorrectly exist which further prevents returns not to be plotted on Security market line. Assumption for single transaction therefore seems reasonable enough to me.

Is it possible to have at a risk free rate in today's world? but in this case it is assumed that such is the case and because the investors to borrow at risk free rate because the individual investor involves more risk as compared to the risk associated with government and resultantly if we are not able to borrow at a risk free rate then the security Market line will be shallower than what we studied in the theory. Regarding the assumption of investors only receiving compensation for systematic risk seems to be very fair to me and is practically acceptable.

In my view the assumptions of the CAPM seem to be idealised slightly than the real view and i think there might be some chances of existence of relationship between required return and Risk.

The equation for CAPM to find the expected rate of return is mentioned below.

E(ri) = Rf + Î²i(E(rm) - Rf)

Explaining the equation .

Rf is the risk free rate and example could be rate of Treasury bill.

Bi is the estimate stock beta, systematic risk.

Rm is the estimate rate of return on market portfolio such as S&P 500 etc.

Example could be suppose risk free rate is 7 percent of a bill , Beta is 1.5 and market portfolio is 13percent. So

E(ri) = 7% = 1.5 ( 13% - 7%)

= 16% out of which seven percent is risk free rate and remaining 9 percent is the risk premium.

ADVANTAGES OF THE CAPM

The CAPM has several advantages over other methods:

As we know that the investors hold a diversified portfolio and the element of unsystematic risk is automatically eliminated, that is why it only considers systematic risk. Many empirical research and tests have showed that it creates a hypothetically derived relationship between required return and systematic risk. Another advantage which makes it superior than others is that it calculates cost of equity by taking into account level of risk with respect to stock market. Discount rates are used in investment appraisal which makes it a better model then weighted average cost of capital.

DISADVANTAGES OF THE CAPM

Besides advantages it also has some disadvantages like in order to compute CAPM we need to assign values to risk free rate of return, the equity risk premium, beta and return on market.The risk free rate of return changes on daily basis according to different conditions prevailing. Proxy beta for the investments must be different from the company's equity beta.If the proxy we selected for the market portfolio isn't efficient enough then it is for sure we wont be able to identify the CML and therefore expected returns using CAPM will be different from the actual figures. So if we use a broad proxy ( broad stock market) for the market portfolio , it would be inappropriate. Moreover proxy companies betas use information that are not easily available.

Other issues regarding estimating Er for individual stocks are.

Dividend adjustments?

It is assumed in CAPM that Market portfolio returns includes dividends. So in my view its necessary to rise a question that the indexes which are made without dividends matter in obtaining greatest estimates so we could have a look whether or not these dividends are included in those index.

frequency and time period ?

As we know regarding estimation that the more observations we take the better the results are. If we follow this then we should be using long time periods as possible. Similarly if we take long estimation period for the beta and it is possible that the value of the actual beta will change over time and the consequential estimate for beta will be prejudiced. Naturally when this happens we will have to shorten the period. Now as we have to collect more observations over shorter time we can do this by increasing the sampling frequency.

As we know CAPM is very precise about the index. Weighted index which consist of all assets in world should be used. As we know that very limited and small portion of assets are traded on the stock exchanges so its not possible to make such a index so we make a proxy instead. Regarding proxy the most commonly used are equal weighted and value weighted index.

There are many of its anomalies which were later on discovered in the 80s and 90s, they in fact became a challenge to the CAPM as the market beta does not suffice to explain expected stock returns. The anomalies were

Earning price ratio.

Size

Leverage

Book to Market equity ratio.

Basu (1977) shows that when common stocks are sorted on earning price ratio , earning price future return on high EP stocks are higher than those predicted by CAPM. Banz (1981) documented about a size effect that stock of small i.e. low market value stocks earned a higher return the predicted by CAPM.small stocks have higher betas and higher returns then large stocks but the difference was more than what was predicted by CAPM. Bhandari ( 1988) illustrated that leverage is positively related to stocks expected returns. As we know that leverage is measured by book value of debt over market value of equity.

Therefore Fama and French (1992) state the earlier findings of other researchers like, higher book to market equity ratios, ratio of book value to market value, have higher returns that are not captured by market beta which is why Fama and French launched a challenge.

CAPM was tested as by taking empirical from large firms from November 1, 2005 to November 1,2006..the information gathered for the stock was for more than 288 public traded companies with market capital more than 500 million dollars , price earning ratio less then 10 and, a greater than zero profitability for over a one year period. The goal was to test the hypothesis that the systematic risk of a portfolio as measured by its market model beta is indeed a relevant measure of risk. The results were there fore found and it was clear that systematic risk as measured by its market beta is not a relevant measure of risk and beta is statically unreliable related to the return of the portfolio. .Therefore it was shown in the research that Capm is not a good model for the calculation of expected return for aggressive portfolios. (Simon G. M. Koo and Ashley Olson)

## The Fama-French three-factor model

This Model as previously discussed was put forward by Fama and French in response to the CAPM in which they think had flaws or deficiencies which were therefore overcome in their model. Fama & French (1992) discussed about the book to market equity ratio, leverage, size and earning to price ratio. A three factor model was therefore proposed by Fama and French for expected returns to show more factors which could be involved and influence the expected returns which the CAPM was not able to include according to them. Variables include the return on stock index, excess returns on portfolio of small stocks above a portfolio of large stocks and excess return on portfolio of high book to market stocks above a portfolio of low book to market stocks.

Following is the equation for computation put forward by them.

(Rit - Rft) = Î±i + Î²1i (Rmt - Rft)+ Î²2i SMBt + Î²3i HMLt + Îµit

In the equation, as discussed before SMB (small minus big) is the difference of the returns on small and big stocks, HML(high minus low) is the difference of the returns on high and low book-to-market equity ratio, and the betas are the factor sensitivities Fama and French argue if asset pricing is rational, size and BE/ME must proxy for risk.SMB notices the element of risk factor related to the size , HML notices the risk factor related to the equity of book to market and market returns. However Fama and French (1992) state that it is improbable as the market betas alone has no power to explain average returns.

Firms which usually follow a tendency of low earning which we may refer to as weak firms over time have high book to market value and there corresponding slopes are positive on High minus low. Similarly firms with a tendency of high earning or strong firms have low book to market value and they project negative slopes on the high minus low . HML basically captures the deviation in the risk factor. Fama and French (1995)

Similarly stocks which possess the property of lower returns with respect to long time periods referred to as the losers tend to have a positive SMB and HML slopes. Reason being that they are small with higher returns in the future. On the other hand stocks with the property of higher long term returns which we may refer to as the winners tend to have negative slopes and low future returns. Market beta is not able to capture the co variation in the returns of small stocks and which is compensated in average returns. (Fama and French)

A Research was made to test Fama and French model and was done by using portfolio from 25 stocks formed on the basis of book / market. Taking observations from 341 different organizations. A test was conducted to find out the standard zero version of the model. The results showed that Fama and French explains better average returns on the 25 portfolios better than CAPM but is not definitely better than CAPM in 30 industries. (Velu and Zhou).

## CONCLUSION

As we have been through both CAPM and Fama and French models to help investors understand the risk/reward tradeoffs which they face when making investments. We talked about CAPM which is famous for its simplicity and is linked to market risk to expected return.

Due to its simple nature it helps to make perception about the returns as a function of risk. Being too simple has also become its weakness as by limited ability to explain and predict the actual returns. Fama and French model enhances the model by including two risk factors SMB and HML. These factors explain that most of the returns due to risk exposure but this model also has certain limitations too.

Many tests have been conducted between both the models to critically analyse the performance of each other .One case of Greek stock exchange and CAPM results showed a non linear relationship between beta and rate of return.CAPM estimation regarding slope and intercept was weak enough and showed poor performance. (Michailias, 2006.).

As there is a lot of evidence against the CAMP these criticisms have increased in the recent years , but in my view CAPM remains a very useful tool in the financial management. Still many investors are in to using CAMP and In my view with these Models investors are able to make more informed investment decisions with respect to personal preference regarding the risk/reward trade-off.

REFERENCING

Bartholdy.J and Peare.P, (2004) , Estimation of expected return:

CAPM vs Fama and French, pp: 1-8.

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French.R and Fama.F (2003), The CAPM: Theory and Evidence, Centre for Research in Security Prices (CRSP) University of Chicago.

French.R and Fama.F ( 1996), The CAPM is Wanted, Dead or Alive, The Journal of Finance, Vol. 51, No. 5.

G. M. Koo Simon and Olson Ashley, Capital Asset Pricing Model Revisited:

Empirical Studies on Beta Risks and Return

Lam Kenneth ,( 2005), Is The Fama-French Three Factor Model Better Than The CAPM,. Pp: 1-6.

Megginson W L,( 1996.) Corporate Finance Theory, Addison-Wesley, p10,

Michailias, G., Tsopoglon, S., and Mariola, E. (2006) Testing the Capital Asset Pricing Model (CAPM): the Case of the Emerging Greek Security Market. International Research Journal of Finance and economics. (Online). Vol (4),pp 78-89. Available from: www.eurojornals.com/finance.hotm. Accessed 13th November 2009.

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Russo. Francesco ( 2005) , CAPM : The challenges of globalization. International Financial Management.

Available at ( http://people.hbs.edu/mdesai/IFM05/Russo.pdf)

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Available at ( http://accounting-financial-tax.com/2010/06/more-advance-with-cost-of-capital-analysis/) accessed November,10th 2010.

Velu.R.and Zhou. G. (1999) Testing Multi-beta Asset Pricing Model, Journal of empirical finance Vol (6), pp 219-241. Available from: www.elsevier.com/locate/man. Accessed :18 Nov 2010